Unless otherwise indicated herein, the materials described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section.
Granular computing refers to computation and operations performed on information granules (group of similar objects or points). Its applicability covers conceptual and computational paradigms of studying information and knowledge processing. Information granules may be constructed specifically in spatial domain and applied to various areas, including automatic target recognition, color image segmentation, and remote sensing image classification. Multispectral remote sensing images may contain information over a large range of variation of frequencies, which may also change over regions. Such data have both spectral features with correlated bands and spatial features correlated in the same band. Simultaneous utilization of the spectral and spatial (contextual) information in an effective manner may enhance the analysis. Methods utilizing the merits of local information in a band for the classification of images, for example, texture features extracted from angular second moments, contrast, correlation, entropy and variance based on the grey-level co-occurrence matrices have found wide applications. However, these methods are typically computationally expensive.
Wavelet transform (WT) is employed as a tool for analyzing texture regions of images, in both spatial (time) and spectral (frequency) domains. Thus, WT may be used for extraction of contextual information of pixels in images by wavelet granulation (i.e., group of similar information in WT domain) of a feature space. Although shift variant WT is quite attractive for various applications, it does not maintain the indispensable property of textural analysis, like time invariance, and makes it insufficient for dealing with texture analysis. Furthermore, the redundant representation of input using WT may increase the feature dimension and bring additional complexity in solving tasks associated with pattern recognition, machine learning and data mining.
Rough set theory has been shown to be an effective tool for feature selection, uncertainty handling, knowledge discovery, and rule extraction from categorical data. The theory enables the discovery of data dependencies and performs the reduction/selection of attributes contained in a data set using the data alone, requiring no additional information. While rough sets may be used as an effective tool to deal with both vagueness and uncertainty in data sets and to perform granular computation, they may be used for numerical data with the discretization of the data, which may result in the loss of information and introduction of noise.